You can get a map of the trails in the jeju tourist centers. There's 4 trails ranging from 1.2 km (I think) to 8.6 km with different starting points. I did the 8.6km in winter and it wasn't that hard, maybe 7.5 hours up and down because one of the member was on the bulky side of things. I reckon 5 hours for fit people.

Bring water and snacks, though they do sell cup ramen at the halfway mark. They also sell hiking gear at decent price at the base, albeit not in my size. I still bought spikes to get through snow slopes. This is for the 8.6km.

Don't show up for the long hike too late as you will need to be back down before the sun is down, if you start at noon they will turn you away at around midpoint probably.

It took us about nine hours, but I don't do tons of hiking. Regular hikers would probably do the round trip much faster. Also, you'll probably want to hang out at the top for a while and take pictures.

Both of my hiking companions were stung by bees, so, you know, watch out for that. Try not to smell like flowers.

I tried it a long time ago from a bus stop on the east side. It was really long and I couldn't do it. I have talked to others who did it by driving to a parking lot a lot closer and went up no problem. If you are thinking about doing it by bus, you might have a much better shot by doing it by driving yourself rather than by bus. This was about 15 years ago though.